On extensions of bounded subgroups in Abelian groups

Commentationes mathematicae Universitatis Carolinae

S. S. Gabriyelyan¹ 

关键词: Abelian group;    bounded group;    simple extension;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

It is well-known that every bounded Abelian group is a direct sum of finite cyclic subgroups. We characterize those non-trivial bounded subgroups $H$ of an infinite Abelian group $G$, for which there is an infinite subgroup $G_0$ of $G$ containing $H$ such that $G_0$ has a special decomposition into a direct sum which takes into account the properties of $G$, and which induces a natural decomposition of $H$ into a direct sum of finite subgroups.

【 授权许可】

CC BY